Answer:
1. Putting x = 0.5, y = -1/10 gives 0.44
2. Putting x = -1, y = -3 gives 14
3. Putting x =3/4 , y = 2/5 gives 1.665
4. Putting x = 0, y = 2.5 gives - 11.25
5. Putting x = √2, y = √2 gives 17
6. Putting x = 2, y = -1 gives - 1
Step-by-step explanation:
-3x2 + 2y2 + 5xy - 2y + 5x2 - 3y2
1. Putting x = 0.5, y = -1/10
-3(0.5)^2 + 2(-1/10)^2 + 5(-0.05) - 2(-1/10) + 5(0.5)^2 - 3(-1/10)^2
= -0.75 +0.02 - 0.25 +0.2 + 1.25- 0.03
= 0.44
2. Putting x = -1, y = -3
-3(-1)^2 + 2(-3)^2 + 5(3) - 2(-3) + 5(-1)^2 - 3(-3)^2
= -3 +18 +15+6+5-27
= 14
3. Putting x =3/4 , y = 2/5
-3(3/4)^2 + 2(2/5)^2 + 5(6/20) - 2(2/5) + 5(3/4)^2 - 3(2/5)^2
=- 27/16 +8/25 +30/20 -4/5 +45/16 - 12/25
= 18/16 - 24/25 + 30/20
= 18/16 - 96+150/100
= 18/16 +54/100
= 1800+ 864/1600
= 2664/1600
=1.665
4. Putting x = 0, y = 2.5
-3(0)^2 + 2(2.5)^2 + 5(0) - 2(2.5) + 5(0)^2 - 3(2.5)^2
= 12.5 - 5.0 - 18.75
= -11.25
5. Putting x = √2, y = √2
-3(√2)^2 + 2(√2)^2 + 5(√2.√2) - 2(√2) + 5(√2)^2 - 3(√2)^2
= -6 +4+10-4+19-6
= 17
6. Putting x = 2, y = -1
-3(2)^2 + 2(-1)^2 + 5(-2) - 2(-1) + 5(2)^2 - 3(-1)^2
= -12+2 -10 +2 +20 -3
= -1
